I purchased a .com domain, but I want to use an independent web. What do I do?

I recently signed up for wordpress and admittedly, I should have done more research before I made a decision. I registered a .com domain name with wordpress for $25. However, I did not realize that I could not upload a custom theme on the normal .com domain. I then looked on the wordpress website for the recommended web hosts and decided to go with Laughing Squid. I signed up with laughing squid, but then afterward, I was told that I cannot change transfer the domain to the independent web host for 60 days. Is this true? In essence, I want to set up a blog at a .com domain, with a custom theme, and webhosting through laughing squid, but I don't know how to do that now that I've already purchased the domain through wordpress.com. I am very new to wordpress and to website creation in general, but I'm trying to learn, so any help would be greatly appreciated. Thank you!
Blog url: http://dapperandwild.wordpress.com/